The object of research is arched bridges made of concrete blocks backfilled with soil. The aim of the study was to develop a technique for determining the arch bridge's optimal shape in order to ensure the required size of the compressed cross-sectional zone at any automobile load position. The calculation takes into account the horizontal and vertical pressure of the backfill soil and the arch dead weight. The concrete blocks can have variable heights. Method. To solve the problem in a physically nonlinear formulation, the stepwise loading method and the possible stress states principle in increments were used. The solution was constructed by the finite element method based on piecewise constant approximations of the moments and forces. The nodes equilibrium equations obtained using the possible displacements principle are added to the additional energy functional written in increments form. The nodes vertical and horizontal displacements are accepted as possible displacements. When determining the required dimensions of the arch, the automobile load all possible positions are considered. Results. The optimum geometric parameters have been determined for an arch bridge with a span of 12 meters. The destructive automobile load value is determined. For the design load, the obtained internal moments and forces are compared with the ones calculated by the program based on the finite element method in displacements.